Research on 3D shape has focused largely on the perception of local geometric properties, such as surface depth, orientation, or curvature. Relatively little is known about how the visual system organizes local measurements into global shape representations. Here, we investigated how the perceptual organization of shape affects the perception of physical stability of 3D objects. Estimating stability is important for predicting object behavior and guiding motor actions, and requires the observer to integrate information from the entire object.

Observers stereoscopically viewed a rendered scene containing a 3D shape placed near the edge of a table. They adjusted the tilt of the object over the edge to set its perceived critical angle, i.e., the angle at which the object is equally likely to fall off the table vs. return to its upright position. The shapes were conical frustums with one of three aspect ratios—either by themselves, or with a part protruding from the side. When present, the boundaries between the part and the frustum were either sharp or smooth. Importantly, the part either faced directly toward the edge of the table or directly away from it.

Observers were close to the physical prediction for tall/narrow shapes, but with decreasing aspect ratio (shorter/wider shapes), there was a tendency to underestimate the critical angle. With this bias factored out, we found that errors were mostly positive when the part faced toward the table's edge, and mostly negative when facing the opposite direction. These results are consistent with observers underestimating the physical contribution of the attached part. Thus, in making judgments of physical stability observers tend to down-weight the influence of attached part—consistent with a robust-statistics approach to determining the influence of a part on global visual estimates (Cohen & Singh, 2006; Cohen et al., 2008).